4,433 research outputs found
Understanding Deutsch's probability in a deterministic multiverse
Difficulties over probability have often been considered fatal to the Everett
interpretation of quantum mechanics. Here I argue that the Everettian can have
everything she needs from `probability' without recourse to indeterminism,
ignorance, primitive identity over time or subjective uncertainty: all she
needs is a particular *rationality principle*.
The decision-theoretic approach recently developed by Deutsch and Wallace
claims to provide just such a principle. But, according to Wallace, decision
theory is itself applicable only if the correct attitude to a future Everettian
measurement outcome is subjective uncertainty. I argue that subjective
uncertainty is not to be had, but I offer an alternative interpretation that
enables the Everettian to live without uncertainty: we can justify Everettian
decision theory on the basis that an Everettian should *care about* all her
future branches. The probabilities appearing in the decision-theoretic
representation theorem can then be interpreted as the degrees to which the
rational agent cares about each future branch. This reinterpretation, however,
reduces the intuitive plausibility of one of the Deutsch-Wallace axioms
(Measurement Neutrality).Comment: 34 pages (excluding bibliography); no figures. To appear in Studies
in the History and Philosophy of Modern Physics, Septamber 2004. Replaced to
include changes made during referee and editorial review (abstract extended;
arrangement and presentation of material in sections 4.1, 5.3, 5.4 altered
significantly; minor changes elsewhere
Being Sure and Being Confident That You Wonât Lose Confidence
There is an important sense in which one can be sure without being certain, i.e., without assigning unit probability. I will offer an explication of this sense of sureness, connecting it with the level of credence that a rational agent would need to have to be confident that she wonât ever lose her confidence. A simple formal result then gives us an explicit formula connecting the threshold α for credence needed for confidence with the threshold needed for being sure: one needs 1â(1âα) to be sure. I then suggest that stepping between α and 1â(1âα) gives a procedure that generates an interesting hierarchy of credential thresholds
Probability in the Everett World: Comments on Wallace and Greaves
It is often objected that the Everett interpretation of QM cannot make sense
of quantum probabilities, in one or both of two ways: either it can't make
sense of probability at all, or it can't explain why probability should be
governed by the Born rule. David Deutsch has attempted to meet these
objections. He argues not only that rational decision under uncertainty makes
sense in the Everett interpretation, but also that under reasonable
assumptions, the credences of a rational agent in an Everett world should be
constrained by the Born rule. David Wallace has developed and defended
Deutsch's proposal, and greatly clarified its conceptual basis. In particular,
he has stressed its reliance on the distinguishing symmetry of the Everett
view, viz., that all possible outcomes of a quantum measurement are treated as
equally real. The argument thus tries to make a virtue of what has usually been
seen as the main obstacle to making sense of probability in the Everett world.
In this note I outline some objections to the Deutsch-Wallace argument, and to
related proposals by Hilary Greaves about the epistemology of Everettian QM.
(In the latter case, my arguments include an appeal to an Everettian analogue
of the Sleeping Beauty problem.) The common thread to these objections is that
the symmetry in question remains a very significant obstacle to making sense of
probability in the Everett interpretation.Comment: 17 pages; no figures; LaTe
Rationality of Belief Or: Why Savage's axioms are neither necessary nor sufficient for rationality, Second Version
Economic theory reduces the concept of rationality to internal consistency. As far as beliefs are concerned, rationality is equated with having a prior belief over a âGrand State Spaceâ, describing all possible sources of uncertainties. We argue that this notion is too weak in some senses and too strong in others. It is too weak because it does not distinguish between rational and irrational beliefs. Relatedly, the Bayesian approach, when applied to the Grand State Space, is inherently incapable of describing the formation of prior beliefs. On the other hand, this notion of rationality is too strong because there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of beliefs.Decision making, Bayesian, Behavioral Economics
Decision-based Probabilities in the Everett Interpretation: Comments on Wallace and Greaves
It is often objected that the Everett interpretation of QM cannot make adequate sense of quantum probabilities, in one or both of two senses: either it cannot make sense of probability at all, or cannot explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections. He argues not only that rational decision under uncertainty makes sense in the Everett interpretation, and that under reasonable assumptions, the credences of a rational agent in an Everett world should be constrained by the Born rule. David Wallace has recently developed and defended Deutsch's proposal, and greatly clarified its conceptual basis. In this note I outline some concerns about the Deutsch argument, as presented by Wallace, and about related proposals by Hilary Greaves. In particular, I argue that the argument is circular, at a crucial point
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